I don't know anyone enough to ask, and I don't know if there's some sort of application process to find one…

There isn't any formal application process to get a co-author. Usually co-authorships are set up rather spontaneously. From my experience (I've co-authored 11 SCP articles) the team-up usually happens during the idea brainstorming phase or early on in the draft process. Basically, a reviewer comes across a draft or an idea that they really like, they discuss it with the author for a couple back-and-forth comments, and they decide to split the work because they both really like the concept.

so I wanted to ask- how do I get one of them?

Write something up and see if anyone likes the idea enough to share the workload with you. That means posting either an ideas thread or a draft thread, and making a note that you'd like to have a co-author to work with if anyone's interested. Again, the important part is that both co-authors need to be invested (and ideally excited about writing) the work.

It's a good idea to have something to bring to the table at the onset, so reviewers/potential co-authors can see what they're committing to. Just saying "I want a co-author for a piece I haven't thought of yet" isn't going to garner you much interest.

Hmm… But what if there was a way to help authors that are open to collaborating link up? Personally, I might never have started writing my own articles for the site if I hadn't began by working with other writers in a group contest.

The two worst-case scenarios for this sort of thing are probably:
1 - "I have a loose idea, someone write it up for me and then stick my name on when you post!"
or, on the other end of the spectrum,
2 - "I want in on your thing! *attach self to coat-tails, don't really contribute*"

Coming up with good ideas for a jumping-off point is something I find difficult, so can't really entice anyone to team up with me that way. But also I really don't want to come off like example #2 here and invite myself in to active projects unwelcomely.

What if there was, like, a forum thread or something to kind of play match-maker for authors trying to collaborate? Maybe self-assess one's strengths and weaknesses, and look for someone willing and able to balance out the partnership? (Should an idea like this go up on the Policy/Proposals forum? For people to suggest how something like that might work best? Or to point out why it mightn't?)

But what if there was a way to help authors that are open to collaborating link up?

That'd pretty much be the forums and chat, from my experience. Pretty much all the co-authored stuff I've done happened because the writer had an idea that the reviewer really liked, and after the reviewer did some concept brainstorming with the writer we just decided to co-author the work so we could both contribute to polishing it.

Personally, I feel like the best co-authored stuff comes out of scenarios where the writer isn't expecting to have a co-author from the get-go. That way, there's more focus on making the draft into something that others would get excited to contribute to, rather than just fishing for that elusive co-author.

(Should an idea like this go up on the Policy/Proposals forum? For people to suggest how something like that might work best? Or to point out why it mightn't?)

I'm actually in the process of writing up a guide on how to co-author works on the site. Ideally it'll be up by the end of the month, but no idea if IRL will cooperate with me on that goal.